Question: $ C = \left[\begin{array}{rr}4 & -2 \\ 1 & -1\end{array}\right]$ $ E = \left[\begin{array}{rr}1 & -1 \\ 2 & 2\end{array}\right]$ Is $ C- E$ defined?
In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ C$ is of dimension $( m \times  n)$ and $ E$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ C$ ) must equal $ p$ (number of rows in $ E$ ) and 2. $ n$ (number of columns in $ C$ ) must equal $ q$ (number of columns in $ E$ Do $ C$ and $ E$ have the same number of rows? Yes Yes No Yes Do $ C$ and $ E$ have the same number of columns? Yes Yes No Yes Since $ C$ has the same dimensions $(2\times2)$ as $ E$ $(2\times2)$, $ C- E$ is defined.